"When one applies for a visa to Australia, for instance, what does the US citizen have to submit to receive a visa/entry permit? "
In most cases US citizens do not need a visa for entry into Australia, all you need is an ETA (Electronic Travel Authority) you fill no forms out, you have no evident visa in your passport and the Australian government has no fee but your airline or travel agent may charge a fee to process it. I went in 2000 and I used evisa to obtain my ETA and the charge was USD 20.
The ETA was set up for citizens of the US and other countries that did not require Australian Citizens to have entry visa's to enter the US etc.
ARRIVAL: Electronic Travel Authority (ETA) for
tourist or business travel, instead of a visa. ETA
applicants do not complete a form and there is no
physical evidence of an ETA in the passport. Existence of
an ETA is verified electronically by ETA participating
airlines prior to boarding and by immigration officials
on arrival in Australia.
Most travel agents issue ETA free of charge whilst
airlines usually charge a handling fee when the passenger
shows up at the check-in counter without visa.